193 citations · 2.8k across the 159 of their papers we have counts for
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Pfaffian point process for the Gaussian real generalised eigenvalue problem
Peter J. Forrester, Anthony Mays
The generalised eigenvalues for a pair of matrices are defined as the solutions of the equation , or equivalently, for invertible,…
Matrix averages relating to the Ginibre ensembles
Peter J. Forrester, Eric M. Rains
The theory of zonal polynomials is used to compute the average of a Schur polynomial of argument , where is a fixed matrix and is from the real Ginibre ensemble. This g…
Derivation of an eigenvalue probability density function relating to the Poincare disk
Peter J. Forrester, Manjunath Krishnapur
A result of Zyczkowski and Sommers [J.Phys.A, 33, 2045--2057 (2000)] gives the eigenvalue probability density function for the top N x N sub-block of a Haar distributed matrix from…
Connection preserving deformations and -semi-classical orthogonal polynomials
Christopher M. Ormerod, Nicholas S. Witte, Peter J. Forrester
We present a framework for the study of -difference equations satisfied by -semi-classical orthogonal systems. As an example, we identify the -difference equation satisfie…
Tridiagonal realization of the anti-symmetric Gaussian -ensemble
Ioana Dumitriu, Peter J. Forrester
The Householder reduction of a member of the anti-symmetric Gaussian unitary ensemble gives an anti-symmetric tridiagonal matrix with all independent elements. The random variables…
Differential equations for deformed Laguerre polynomials
Peter J. Forrester, Christopher M. Ormerod
The distribution function for the first eigenvalue spacing in the Laguerre unitary ensemble of finite size may be expressed in terms of a solution of the fifth Painleve transcenden…